Towards New Classes of Flux Compactifications

We derive novel solutions of flux compactification with D7-branes on the resolved conifold in type IIB String Theory and later extend this solution to allow for non-zero temperature. At zero temperature, we find that adding D7-branes via the Ouyang embedding contributes to the supersymmetry-breaking (1,2) imaginary-self-dual flux, without generating a bulk cosmological constant. We further find that having D7-branes and a resolved conifold together give rise to a non-trivial D-term on the D7-branes. This supersymmetry-breaking term vanishes when we take the singular conifold limit, although supersymmetry appears to remain broken. We also lift our construction to F-theory where we show that the type IIB (1,2) flux goes to (2,2) non-primitive flux on the fourfold. In the second part of the thesis, we extend these results by taking the non-extremal limit of our geometry to incorporate temperature. In this case, the internal NS-NS and R-R fluxes are no longer expected to be self-dual, but they should also naturally be extensions of the fluxes found above. From the supergravity equations of motion, we compute how the new contributions to the fluxes should enter, due to the squashing of the resolved metric and non-extremality. This provides us with a compelling gravity dual of large N thermal quantum chromodynamics with flavor